The article discusses the issues of quality control, and primarily fracture of granite blocks in the process of their extraction in the quarries of North-West region of Russia. Analyzes the causes of fracture, its influence on strength of granite products recommended instruments for its detection. Focuses on the causes of fracture of the granites in the process of their extraction methods of diamond cutting and using explosion. Recommended certified and made in the state register of Russia measurement tools allow you to control the defects by the method of the anchor dug, devices for measuring the frequency of oscillations of products from granite, allowing its value to control the presence of defects in the samples, instruments for measuring humidity granites.

Keywords: Granites, defects, granite mining, quarry, quality, quality control, fracturing, the technology of extraction of granite

A financial market on a stochastic basis with a filtration generated by the binary tree is considered. A plugin simulating failures on this market is constructed. We mean by a failure the following situation on the financial market: when passing from a time moment  to the next one new events arise but discounted price of the fixed type stock does not change. A failure generates the incompleteness of the market (the set of martingale measures of this market is infinite). By modelling of a weak deformation it is possible to reduce the set of martingale measures to a unique measure. Thereby the price of every contingent claim is uniquely determined. This price may be considered as "fair price".

Keywords: Stochastic basis, probability measure, financial market, binary tree, arbitrage free, completeness, weak deformation, martingale measure, plugin.

With the help of so-called deformations (that is of probability measures families on sigma-fields forming a filtration) a notion of deformed martingale is introduced. This notion generalizes the classical concept of martingale with discrete time. We differ two sorts of deformed martingales: deformed martingales of the 1-st and the 2-nd type. Similarly deformed sub- and supermartingales of the 1-st and the 2-nd type are introduced. We prove that infimum of arbitrary family of deformed supermartingales is a supermartingale and that convexe function of deformed martingale is a deformed submartingale. In addition, for deformed martingales of the 2-nd type a telescopic property is obtained.

Keywords: Filtration, probability measure, deformation, deformed martingale, telescopic property

We consider a one-step part (B, S) - a market with an infinite number of states. The first part of the article deals with modeling of random behavior of an infinite number of aggressive buyers of the shares in the financial market. There will be described one way to exit the buyers of shares on the market, the gap between the announcement of the share price. In the second part of the article presents the procedure hedge payment obligation (bp), which uses interpolation of incomplete full-arbitrage market economies (Haar interpolation method).

Keywords: Stochastic basis, financial market, martingale measure,the weakened property of the universal Haar uniqueness, self-financing portfolios, capital of portfolio, contingent claim.

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In this paper, the task of achieving the optimal bandwidth telecommunication channels. Focuses on technical aspects of managing bandwidth channels using virtual organization switched channels. Formally defined parameters affecting the guaranteed delivery service. A model and management solution parameters guaranteed delivery of information in the communication channels, based on the methods of the theory of stochastic processes theory and risk analysis.
Keywords: reliability of telecommunication systems, telecommunication systems modeling, stochastic processes, optimal risk management.

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